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Page No 12.46:
Question 1:
From the data given below, construct the index number for the year 2016 on the base of 2011 by simple aggregative method:
Commodities | Unit | Price (In â¹) | |
2011 | 2016 | ||
Wheat | quintal | 200 | 250 |
Rice | quintal | 300 | 400 |
Pulses | quintal | 400 | 500 |
Milk | litre | 2 | 3 |
Clothing | meter | 4 | 5 |
Answer:
Commodity | Price in 2011 (P0) |
Price in 2016 (P1) |
Wheat Rice Pulses Milk Clothing |
200 300 400 2 4 |
250 400 500 3 5 |
ΣP0 = 906 | ΣP1 = 1158 |
Page No 12.47:
Question 2:
Construct index numbers by (aggregative method) based on the price of 2011 from the following figures:
Items | A | B | C | D | E | F |
Prices (2011) | 200 | 60 | 350 | 100 | 60 | 80 |
Prices (2019) | 240 | 90 | 600 | 110 | 62 | 90 |
Answer:
Items | Price in 2011 (P0) |
Price in 2019 (P1) |
A B C D E F |
200 60 350 100 60 80 |
240 90 600 110 62 90 |
ΣP0 = 850 | ΣP1 = 1192 |
Page No 12.47:
Question 3:
Following are the prices of commodities in the year 2011 and 2019. Calculate the price index using price relatives method.
Commodity | Prices in year 2011 | Prices in 2019 |
A | 45 | 55 |
B | 60 | 70 |
C | 20 | 30 |
D | 50 | 75 |
E | 85 | 90 |
F | 120 | 130 |
Answer:
Commodity | Price in 2011 (P0) |
Price in 2019 (P1) | Price Relative= |
A | 45 | 55 | |
B | 60 | 70 | |
C | 20 | 30 | |
D | 50 | 75 | |
E | 85 | 90 | |
F | 120 | 130 | |
Page No 12.47:
Question 4:
4. Calculate the index numbers from the following data using:
(i) Laspeyre's method,
(ii) Paasche's method,
(iii) Fisher's ideal method:
Commodity | Base year | Current year | ||
Price (in â¹) p | 0Quantity q0 | Price (in â¹) p1 | Quantity q1 | |
A | 8 | 100 | 10 | 120 |
B | 4 | 60 | 5 | 80 |
C | 10 | 20 | 12 | 25 |
D | 12 | 25 | 15 | 30 |
E | 3 | 5 | 4 | 6 |
Answer:
Base Year | Current Year | |||||||
Commodity | Price p0 |
Quantity q0 |
Price p1 |
Quantity
q1
|
p0q0 | p0q1 | p1q0 | p1q1 |
A | 8 | 100 | 10 | 120 | 800 | 960 | 1000 | 1200 |
B | 4 | 60 | 5 | 80 | 240 | 320 | 300 | 400 |
C | 10 | 20 | 12 | 25 | 200 | 250 | 240 | 300 |
D | 12 | 25 | 15 | 30 | 300 | 360 | 375 | 450 |
E | 3 | 5 | 4 | 6 | 15 | 18 | 20 | 24 |
Σp0q0 = 1555 | Σp0q1 = 1908 | Σp1q0 = 1935 | Σp1q1 = 2374 |
(i) Laspeyre's Method
(ii) Paasche's Method
(iii) Fisher's Method
Page No 12.47:
Question 5:
Calculate Laspeyre's; Paasche's and Fisher's index numbers from the following data:
Commodity | Base year | Current year | ||
Price (in â¹) p0 | Quantity q0 | Price (in â¹) | Quantity q1 | |
A | 10 | 30 | 12 | 50 |
B | 8 | 15 | 10 | 25 |
C | 6 | 20 | 6 | 30 |
D | 4 | 10 | 6 | 20 |
Answer:
Base Year | Current Year | |||||||
Commodity | Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
p0q0 | p0q1 | p1q0 | p1q1 |
A | 10 | 30 | 12 | 50 | 300 | 500 | 360 | 600 |
B | 8 | 15 | 10 | 25 | 120 | 200 | 150 | 250 |
C | 6 | 20 | 6 | 30 | 120 | 180 | 120 | 180 |
D | 4 | 10 | 6 | 20 | 40 | 80 | 60 | 120 |
Σp0q0 = 580 | Σp0q1 = 960 | Σp1q0 = 690 | Σp1q1 = 1150 |
(i) Laspeyre's Method
(ii) Paasche's Method
(iii) Fisher's Method
Page No 12.48:
Question 6:
The following table contains information from the raw material purchase records of a small factory to the year 2011-12 and 2019-20:
Commodity | 2011-12 | 2019-20 | ||
Price (â¹/Unit) p0 | Total Valule q0 | Price (â¹/Unit) | Total Value q1 | |
A | 5 | 50 | 6 | 72 |
B | 7 | 84 | 10 | 80 |
C | 10 | 80 | 12 | 96 |
D | 4 | 20 | 5 | 30 |
E | 8 | 56 | 8 | 64 |
Answer:
Base Year
(2011-12)
|
Current Year (2019-20) |
|||||||
Commodity | Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
p0q0 | p0q1 | p1q0 | p1q1 |
A | 5 | 50 | 6 | 72 | 250 | 360 | 300 | 432 |
B | 7 | 84 | 10 | 80 | 588 | 560 | 840 | 800 |
C | 10 | 80 | 12 | 96 | 800 | 960 | 960 | 1152 |
D | 4 | 20 | 5 | 30 | 80 | 120 | 100 | 150 |
E | 8 | 56 | 8 | 64 | 448 | 512 | 448 | 512 |
Σp0q0 = 2166 | Σp0q1 = 2512 | Σp1q0 = 2648 | Σp1q1 = 3046 |
Fisher's Method
Page No 12.48:
Question 7:
Calculate weighted average of price relative index number of prices for 2019 on the basis of 2011 from the following data:
Comity | Quantity in 2011 | Price (in â¹)2011 | Price (in â¹) 2019 |
A | 20 | 20 | 35 |
B | 12 | 15 | 18 |
C | 8 | 10 | 11 |
D | 4 | 5 | 5 |
E | 6 | 4 | 5 |
Answer:
Commodity | Quantity in 2011 (q0) Weights |
Price in 2011 (p0) |
Price in 2019 (p1) |
p0q0 (W) |
R= |
RW |
A | 20 | 20 | 35 | 400 | 175 | 70000 |
B | 12 | 15 | 18 | 180 | 120 | 21600 |
C | 8 | 10 | 11 | 80 | 110 | 8800 |
D | 4 | 5 | 5 | 20 | 100 | 2000 |
E | 6 | 4 | 5 | 24 | 125 | 3000 |
ΣW = 704 | ΣRW = 105400 |
Weighted Average of Price Relatives
Page No 12.48:
Question 8:
Construct cost of index number for 2019 on the basis of 2011 from the following data using Aggregate Expenditure Method and Family Budget Method.
Article | Quantity (kg.) | Prices in â¹ | |
2011 | 2019 | ||
A | 10 | 20 | 30 |
B | 7 | 21 | 28 |
C | 5 | 20 | 25 |
D | 2 | 10 | 12 |
E | 2 | 6 | 8 |
Answer:
Article | Price in 2011 (p0) |
Price in 2019 (p1) |
Quantity
(q0)
|
p0q0 | p1q0 |
A | 20 | 30 | 10 | 200 | 300 |
B | 21 | 28 | 7 | 147 | 196 |
C | 20 | 25 | 5 | 100 | 125 |
D | 10 | 12 | 2 | 20 | 24 |
E | 6 | 8 | 2 | 12 | 16 |
Σp0q0 = 479 | Σp1q0 = 661 |
Consumer price index for the year 2016
Article | Price in 2011 (p0) |
Price in 2016 (p1) |
Price Relative (R) |
Quantity (q0) |
p0q0 (W) |
RW |
A | 20 | 30 | 150 | 10 | 200 | 30000 |
B | 21 | 28 | 133.33 | 7 | 147 | 19599.51 |
C | 20 | 25 | 125 | 5 | 100 | 12500 |
D | 10 | 12 | 120 | 2 | 20 | 2400 |
E | 6 | 8 | 133.33 | 2 | 12 | 1599.96 |
ΣW = 479 | ΣRW = 66099.47 |
Consumer price index for the year 2016
Page No 12.48:
Question 9:
Calculate consumer price index number for the following data by aggregate expenditure and family budget Method.
Expenses | Weights | Price (in â¹) Base Year | Price (in â¹) Current year |
Food | 45 | 300 | 350 |
Rent | 20 | 200 | 225 |
Fuel | 8 | 100 | 110 |
Clothing | 10 | 150 | 175 |
Misc. | 17 | 250 | 300 |
Answer:
Expenses | Price in Base Year (p0) |
Price in Current Year (p1) |
Quantity (q0) |
p0q0 | p1q0 |
Food | 300 | 350 | 45 | 13500 | 15750 |
Rent | 200 | 225 | 20 | 4000 | 4500 |
Fuel | 100 | 110 | 8 | 800 | 880 |
Clothing | 150 | 175 | 10 | 1500 | 1750 |
Misc. | 250 | 300 | 17 | 4250 | 5100 |
Σp0q0 = 24050 | Σp1q0 = 27980 |
Consumer price index for the current year
Expenses | Price in Base Year (p0) |
Price in Current Year (p1) |
Quantity (q0) |
p0q0 (W) |
RW | |
Food | 300 | 350 | 116.67 | 45 | 13500 | 1575045 |
Rent | 200 | 225 | 112.5 | 20 | 4000 | 450000 |
Fuel | 100 | 110 | 110 | 8 | 800 | 88000 |
Clothing | 150 | 175 | 116.67 | 10 | 1500 | 175005 |
Misc. | 250 | 300 | 120 | 17 | 4250 | 510000 |
ΣW= 24050 | ΣRW = 2798050 |
Consumer price index for the current year
Page No 12.49:
Question 10:
Construct the index of industrial production from the following data:
Commodity | Output (in tonnes) | Weights | |
2011-12 | 2019-20 | ||
Mining | 120 | 180 | 25 |
Electrical Products | 200 | 290 | 45 |
Manufactured Goods | 150 | 220 | 30 |
Answer:
Industry | Output in 2011-12 (q0) |
Output in 2019-20 (q1) |
Weights (W) |
||
Mining | 120 | 180 | 25 | 150 | 3750 |
Electrical Products | 200 | 290 | 45 | 145 | 6525 |
Manufactured Goods | 150 | 220 | 30 | 146.67 | 4400.1 |
ΣW=100 | 14675.1 |
Index Number of Industrial Production
Page No 12.49:
Question 11:
Calculate the cost of living index number for 2019 taking 2012 as base year from the following data by family budget Method.
Times | Quantity (in kg.) | Price 2012 (in â¹/kg) | Price 2019 (in â¹/kg) |
A | 15 | 10.00 | 12.00 |
B | 20 | 16.50 | 20.00 |
C | 8 | 6.00 | 7.50 |
D | 12 | 15.00 | 16.00 |
E | 10 | 8.00 | 11.50 |
Answer:
Items | Price | Price Relative (R) |
Quantity | |||
2012 (p0) |
2019 (p1) |
2012 (q0) |
p0q0 (W) |
RW | ||
A | 10.00 | 12.00 | 120.00 | 15 | 150 | 18000.0 |
B | 16.50 | 20.00 | 121.21 | 20 | 330 | 39999.3 |
C | 6.00 | 7.50 | 125.00 | 8 | 48 | 6000.0 |
D | 15.00 | 16.00 | 106.67 | 12 | 180 | 19200.6 |
E | 8.00 | 11.50 | 143.75 | 10 | 80 | 11500.0 |
ΣW = 788 | ΣRW = 94699.9 |
Page No 12.49:
Question 12:
The following data relate to the prices and quantities of 4 commodities in the years 2011-12 and 2019-20. Construct the index numbers of price for the year 2019-20 by using 2011-12 the base year by: (i) Laspeyre's method, (ii) Paasche's method, (iii) Fisher's ideal method:
Commodity | 2011-12 | 2019-20 | ||
Price (in â¹) p0 | Quantity q0 | Price (in â¹) | Quantity q1 | |
A | 5 | 100 | 6 | 150 |
B | 4 | 80 | 5 | 100 |
C | 2.5 | 60 | 5 | 72 |
D | 12 | 30 | 9 | 33 |
Answer:
Commodity | p0 | q0 | p1 | q1 | p0q0 | p0q1 | p1q0 | p1q1 |
A | 5 | 100 | 6 | 150 | 500 | 750 | 600 | 900 |
B | 4 | 80 | 5 | 100 | 320 | 400 | 400 | 500 |
C | 2.5 | 60 | 5 | 72 | 150 | 180 | 300 | 360 |
D | 12 | 30 | 9 | 33 | 360 | 396 | 270 | 297 |
Total | 1330 | 1726 | 1570 | 2057 |
(i) Laspeyre's Method
(ii) Paasche's Method
(iii) Fisher's Method
Page No 12.49:
Question 13:
Calculate the index number for 2019 with 2012 as base using the weighted average of price relative method for the following data:
Commodity | Quantity (in units) 2012 | Price (in â¹)2012 | Price (in â¹)2019 |
A | 2 | 12 | 24 |
B | 8 | 8 | 12 |
C | 4 | 15 | 27 |
D | 5 | 6 | 18 |
E | 1 | 10 | 12 |
Answer:
Commodity | 2012 q0 |
2012 p0 |
2019 p1 |
p0q0 (W) |
Price Relative (R)= |
RW |
A | 2 | 12 | 24 | 24 | 200 | 4800 |
B | 8 | 8 | 12 | 64 | 150 | 9600 |
C | 4 | 15 | 27 | 60 | 180 | 10800 |
D | 5 | 6 | 18 | 30 | 300 | 9000 |
E | 1 | 10 | 12 | 10 | 120 | 1200 |
ΣW = 188 | ΣRW = 35400 |
Weighted Average of Price Relatives
Page No 12.50:
Question 14:
Construct an index for the year 2019 taking 2011 as base by simple average of price relatives method
Items | P | Q | R | S |
Price (in â¹) | 30 | 50 | 70 | 90 |
Price (in â¹) | 40 | 60 | 80 | 100 |
Answer:
Items | Price in 2011 (P0) |
Price in 2019
(P1)
|
Price Relative= |
P | 30 | 40 | 133.33 |
Q | 50 | 60 | 120 |
R | 70 | 80 | 114.29 |
S | 90 | 100 | 111.11 |
Simple Average of Price Relatives
Page No 12.50:
Question 15:
Using Paasche's formula, compute the quantity index for the year 2019 with 2011 as base year.
Commodity | Quantify (in Units) | Value (in â¹) | ||
2011 | 2019 | 2011 | 2019 | |
A | 5 | 100 | 6 | 150 |
B | 100 | 150 | 500 | 900 |
C | 80 | 100 | 320 | 500 |
D | 60 | 72 | 150 | 360 |
E | 30 | 33 | 360 | 297 |
Answer:
Commodity | Quantity in 2011 (q0) |
Quantity in 2019 (q1) |
Price in 2011 (p0) |
Price in 2019 (p1) |
q1p1 | q0p1 |
A | 5 | 100 | 6 | 150 | 15000 | 750 |
B | 100 | 150 | 500 | 900 | 135000 | 90000 |
C | 80 | 100 | 320 | 500 | 50000 | 40000 |
D | 60 | 72 | 150 | 360 | 25920 | 21600 |
E | 30 | 33 | 360 | 297 | 9801 | 8910 |
235721 | 161260 |
Note: As per the textbook, the quantity index is 119.177. However, as per the above solution quantity index should be 146.17.
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